Problem: Simplify the following expression: $\sqrt{63}+\sqrt{28}+\sqrt{175}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{63}+\sqrt{28}+\sqrt{175}$ $= \sqrt{9 \cdot 7}+\sqrt{4 \cdot 7}+\sqrt{25 \cdot 7}$ Separate the radicals and simplify. $= \sqrt{9} \cdot \sqrt{7}+\sqrt{4} \cdot \sqrt{7}+\sqrt{25} \cdot \sqrt{7}$ $= 3\sqrt{7}+2\sqrt{7}+5\sqrt{7}$ Finally, simplify by combining the terms. $= ( 3 + 2 + 5 )\sqrt{7} = 10\sqrt{7}$